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How to Calculate Percentages

Knowing how to calculate percentages will help you not only score well on a math test but in the real world as well. They are used for calculating tips in restaurants, finding out the nutritional content of your food, or even determining statistics of your favorite sports team. Regardless of how you plan to use the knowledge, calculating percentages is fundamental and quite easy overall.

Visualize what a percentage represents. A percentage is an expression of part of the whole. Nothing is represented by 0%, and the whole amount is 100%. Everything else is somewhere in between![1]

For example, say you have 10 apples. If you eat 2 apples, then you have eaten 2 out of the whole 10 apples (2 / 10 × 100% = 20% eaten). If 10 apples is 100% and you ate 20%, then 100% - 20% = 80% of the apples remain.

The term "percent" in English comes from the Latin per centum, meaning “through 100” or “for 100”.

The percentage symbol is merely a format. In statistics, percentages are often left in their base form of 0 - 1, where 1 represents the whole. We merely multiply a decimal by a factor of 100% to format the answer.

Determine the value of the whole. In some cases, you will be given the value for part of the whole and the whole. Other times, you might get two parts that make up the whole. It is important to distinguish what the percentage is “of.” For instance, let's say we have a jar containing 1199 red marbles and 485 blue marbles, making it 1684 marbles in total. In this case, 1684 makes up a whole jar of marbles, i.e. 100%.[2]

Find the value that you want to turn into a percentage. Let's say we want to find out the percentage of the jar that is taken up by the blue marbles. Then the percentage of the whole we are looking for is 485 (the number of blue marbles) of 1684 (the whole amount).[3]

Convert the fraction into a decimal. Percentages are best calculated from the decimal form. To turn 485/1684 into a decimal, divide 485 by 1684 using a calculator or pencil and paper. This comes to 0.288.[5]

Identify the given numbers you're working with. Say you borrowed money from a friend who is going to charge you daily interest. The amount borrowed was initially $15 and the interest rate is 3% per day. These are the only two numbers you need for the calculation.[7]

Convert the percentage into a decimal. Working backward from before, divide the percentage by 100%, or you can multiply by 0.01 (they’re the exact same). 3%/100% = 3/100 = 0.03. You can also simply move the decimal to the left two places.[8]

Re-word the problem with your new values. It helps to reword your problem with the new value(s) now in the form of “X of Y is Z.” X is the decimal form of your percent, “of” means to multiply, Y is the whole amount, and Z is the answer. So, 0.03 x $15 is $0.45.[9]

In this example, $0.45 is the amount of interest accrued each day that you do not pay your friend back.

If you need to further calculate the total due after 1 day, you would add the amount you borrowed to the amount of the interest times the number of days. So $15 + ($0.45 x 1 day) = $15.45.

Write down the original price and the discount percentage. The original price is usually the big number that retailers will mark through or make especially large so you know how good of a “deal” you’re getting.[10]

Be sure to also pay attention to whether the discounted percentage applies to a single item or the total.

If it is the total, you would add up all the original prices to get your whole amount to which you apply the percentage discount. Otherwise, you will only apply the discount to the single original price.

Find the opposite of the discount percentage. This trick lets you perform 1 calculation instead of 2! The opposite of a percent is 100% minus the percent you are working with, i.e. the amount of the item you are still paying for. If you want to buy a shirt that is 30% off, the opposite of this is 70%, meaning you would have to pay 70% of the original price.[11]

Convert the opposite percent into a decimal. To convert a percent into a decimal, divide by 100%, multiply times 0.01, or move the decimal two places to the left. In this example, 70%/100% = 70/100 = 7/10 = 0.7.[12]

Calculate your savings afterward to feel better. Once you get home, it can be a good idea to check your receipts, not only to make sure the discounts were applied correctly but to see how much you saved altogether. Here, you can simply subtract the sale price from the original price ($20 - $14 = $6 saved)!

To calculate the percentage increase, work out the difference (increase) between the two numbers you are comparing. Then divide the increase by the original number and multiply the answer by 100. If your answer is a negative number, then this is a percentage decrease.

First you need to calculate what number the percentage is equal to. Do this by converting the percentage to a decimal and then multiplying the decimal by the original number. Now you can add this answer to the original number.

About This Article

To calculate percentages, start by writing the number you want to turn into a percentage over the total value so you end up with a fraction. Then, turn the fraction into a decimal by dividing the top number by the bottom number. Finally, multiply the decimal by 100 to find the percentage.